9701142 Weaver A project is to be undertaken to further our understanding of linear stochastic wave fields, waves which have suffered sufficient randomizing scatterings or reflections as to lose most coherence. Such fields are present in applications of ultrasonics in many modern heterogeneous materials. The proposed work primarily concerns the diffuse ultrasonics of polycrystalline materials with a view towards ultimate applications in robust ultrasonic characterization of microstructures and flaw detection in the midst of grain noise. The main focus will be towards the validation of ultrasonic radiative transfer formulations of multiple diffuse scattering in polycrystals. Of particular interest is the transition from the simple single scattering limit model used by many, through the complicated regime in which typical rays have scattered a few times, to the once again simple diffusion limit in which typical rays have scattered many times. Broad industrial Interest in materials characterization where conventional attenuation and velocity measurements are difficult or fail, and where therefore the proposed project will have application, includes grain size and texture characterization through rough surfaces (with associated inferences in regard to fracture toughness and formability), detection of low levels of porosity in acoustically (grain-)noisy materials with thick sections (i.e. porosity in powder metallurgical iron), detection of microcracking and monitoring of microcracking after service, detection and monitoring of embrittling conditions, detection of residual stresses, and characterization of highly inhomogeneous materials such as sintered materials or metallic foams. While the primary concern and envisioned Immediate application i s in diffuse ultrasonics, fields of this kind are also present on sufficiently long time scales In seismology, in reverberation rooms, In the vibrations of large Irregular built structures, In the electronics of mesoscale devices and for optics in turbid media. The project Is also, therefore, expected to contribute to these other fields. The proposed project consists of theory, numerics, and experiments. The equations of ultrasonic radiative transfer will be extended where necessary. They will be applied to the specific experimental configurations and samples to be studied in the lab. The resulting numerically generated predictions for diffuse ultrasonic intensity will be compared with laboratory measurements and with direct numerical simulations of two-dimensional heterogeneous elastic media. Extensive ultrasonic Immersion testing of metal samples with well controlled polycrystalline microstructures will be carried out in a variety of configurations designed to be optimal for illustrating and testing the main predictions of radiative transfer. Two secondary but related thrusts will be carried out also. One on ultrasound in materials with extremely strongly scattering microstructures will contribute to a basic understanding of fluctuations and transport in materials with attenuations of the order of wavenumbers. The other on reverberant ultrasound at very late times will study fields which are potentially very sensitive to global properties of the samples in which they reverberate. The proposed methods are expected to reveal material properties that are not otherwise easily obtained. This is a collaborative project In which the theory and numerics will be conducted primarily at the University of Illinois, and the experiments will be conducted primarily at the Uni versity of Missouri.
